Probabilistic solution of Pauli type equations

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Abstract
Extends the Feynman-Kac formula to the case of imaginary time Schrodinger equations (heat equations) for multicomponent wavefunctions. The approach covers in particular the usual Pauli equation for a spin-1/2 particle in an arbitrary magnetic field. The formula contains, besides the expectation with respect to a Wiener process in ordinary space, an expectation with respect to a jump process over the discrete indices describing the internal degrees of freedom. To illustrate the method the authors evaluate the formula in some special cases and they derive also various inequalities. A detailed comparison is made with a recent work by Gaveau and Vauthier (1981).

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